Last updated : 28th July 2005

List of some Recent Publications of Isaak A. Kunin pertaining to his work in Nonlinear Dynamics:
( number is the publication number from Prof. Kunin's curriculum vitae listed on his website above)

For reprints contact : kunin AT uh.edu OR ciyyunni AT uh.edu

177. S. Preston, I. Kunin, Yu. Gliklikh, G. Chernykh, "On the Geometrical Aspects of Chaotic Dynamics",International Journal of Engineering Science, v 41, 2003, pp 495-506.

176. V. Kreinovich, I. Kunin, "Kolmogorov Complexity and chaotic Phenomena",International Journal of Engineering Science, v 41, 2003, pp 483-493.

175. B. Yamrom, I. Kunin, G. Chernykh, "Method of algorithmic transformations with applications to chaotic systems",International Journal of Engineering Science, v 41, 2003, pp 475-482.

174. Yamrom, B. , Kunin, I.; Chernykh, G., "Centroidal Trajectories and Frames for Chaotic Dynamical Systems", International Journal of Engineering Science,  v 41, 2003, p 465-473.

173. Kunin, I. Hussain, F.; Zhou, X., "On multiple routes to chaos in advection induced by point vortices", International Journal of Engineering Science,  v 41, n 3-5,  March, 2003, p 459-464
Abstract: Chaotic advection induced by periodic motions of point vortices inside and outside of a circular domain and in the infinite plane is analyzed. Though simple, this model flow captures multiple routes to chaos and gives a good qualitative picture of advection in more complicated domains such as rectangle and ellipse. Different scenarios of chaotic advection depend on the topology of unperturbed phase portraits and type of perturbations. In addition to the typical KAM cases, we find scenarios accounting for inherent singularity of the velocity field. (13 refs.)

172. Yamrom, B. , Kunin, I.; Metcalfe, R.; Chernykh, G., "Discrete systems of controlled pendulum type", International Journal of Engineering Science,  v 41, n 3-5,  March, 2003, p 449-458
Abstract: A challenging class of controlled pendulum (CP) type systems has been introduced in [I.A. Kunin, B. Kunin, Proc. 39th Annual Conf. Soc. Eng. Sci., Penn State University, University Park, PA, October 2002] in which examples have been computed using standard floating-point methods. This work deals with recently developed discrete methods [B.Yamrom, I.A. Kunin, G.A. Chernykh, Proc. 39th Annual Conf. Soc. Eng. Sci., Penn State University, University Park, PA, October 2002; I.A. Kunin, N. Shamsundar, R.W. Metcalfe, A Discrete Approach to Continuous Chaotic Systems, in preparation] applied to the same CP type systems in order to compare results using the two approaches and to address the issue of extracting additional information about the system that cannot readily be obtained using floating-point methods. These include such features as discrete cycles and transients leading to such cycles. (8 refs.)

171. Kunin, I., Kunin, B.; Chernykh, G. "Lorenz-type controlled pendulum", International Journal of Engineering Science,  v 41, n 3-5,  March, 2003, p 433-448
Abstract: It is known that the popular Lorenz system admits an equivalent representation as a controlled Duffing system. It is also known that the Duffing system is an approximation to the simple pendulum. We introduce a new class of controlled pendulum systems that may also be interpreted as Pendulum-Lorenz systems. These systems contain the Lorenz system as an approximation and have a wide range of potential applications. Examples of chaotic attractors associated with a controlled pendulum system are presented. © 2002 Elsevier Science Ltd. All rights reserved. (11 refs.)

170. Kunin, I., "On extracting physical information from mathematical models of chaotic and complex systems",  International Journal of Engineering Science,  v 41, n 3-5,  March, 2003, p 417-432
Abstract: The paper describes a multi-structural approach to the problem indicated in the title. In analogy with quantum mechanics, at the core of the approach are two notions: states and (generalized) observables. This motivates us to distinguish between mathematical and physical dynamical systems. The first class deals with mathematical models and states (solutions) only. The second one adds physical realizations and observables, i.e. all methods of extracting useful information. Observables include: renormalization, optimal gauging, covering-coloring, discretization, tensorial measures of chaos, etc. The corresponding algorithms are correlated to Kolmogorov complexity and are intrinsic parts of observables, and thus of physical systems. The approach is illustrated by examples. © 2002 Elsevier Science Ltd. All rights reserved. (27 refs.)

I. Kunin, A. Runov, "A class of Lorenz-type systems, their factorizations and extensions, arXiv:math .DS /0105149v1, 17 May 2001.

Kunin, I. , Hussain, F.; Zhou, Z.; Kovich, D.,"Dynamics of point vortices in a special rotating frame", International Journal of Engineering Science,  v 28, n 9, 1990, p 965-970
Abstract: A special rotating frame (SRF) is found in which the relative motion of point vortices is simpler, has minimum energy and reveals dynamical features not discernible in the usual fixed frame. The angular velocity of this frame is a solution of the equations of motion and generally is not constant. Examples of periodic, quasiperiodic and chaotic motions with respect to the SRF show that: (a) periodic orbits are closed lines (not space filling as in the fixed frame, (b) quasiperiodic orbits form steady patterns and (c) chaotic motions create asymptotic symmetries that reflect permutation symmetry of the Hamiltonian. (8 refs.)

Preston, Serge , Kunin, I.; Gliklikh, Y.E.; Chernykh, G.,"On the geometrical characteristics of chaotic dynamics, I", International Journal of Engineering Science,  v 41, n 3-5,  March, 2003, p 495-506
Abstract: The geometrical characteristics of chaotic dynamics were presented. It was found that these structures carry important information about the properties of dynamical system: all curvatures of trajectories, Lyapunov exponents etc. The numerical calculations of curvatures of eigenvalues of these tensors along trajectories of Lorentz system displayed sharp change of behavior near the points where trajectories leave the fractal surface of attractor. (12 refs.) (Edited abstract)

141. Kunin, I., "Duffing Lorenz type systems", International Conference in honor of V. Arnold, 1997, The Fields Institute, Toronto, Canada.

139. Kunin, I.; Prishepionok, S.,"G-moving frames and their applications in dynamics", International Journal of Engineering Science,  v 33, n 15,  Dec, 1995,  Edelen Symposium, p 2261
Conference: Proceedings of the 31st Annual Technical Meeting of the Society of Engineering Science, Oct 10-12 1994, College Station, TX, USA